Nucleation of cracks in an isotropic medium with periodic system of rigid inclusions under transverse shear

Abstract

A model of nucleation of cracks in composite materials with periodic structures is given. The model is based on the analysis of the cracking zone. It is assumed that the zone cracking is a layer of finite length with weakened bonds between the material particles. The interaction of pre-fracture zone surfaces is modeled by applying cohesive forces caused by bonds to pre-fracture zone surfaces. The analysis of the limit equilibrium of pre-fracture zones under transverse shear involves (i) a definition of relationships between cohesive forces and surfaces pre-fracture zone shear; (ii) the evaluation of displacement and stresses around the pre-fracture zone taking account of external loads and cohesive forces, also disposition of rigid inclusions; (iii) definition of the dependence of critical external loads under which the nucleation of a crack occurs on geometric parameters of the medium. The condition for the appearance of a crack is formulated taking account the criterion of the limit traction of the bonds in the material.